Optimal. Leaf size=66 \[ -\frac{648 x^5}{625}+\frac{513 x^4}{625}+\frac{2826 x^3}{3125}-\frac{7617 x^2}{6250}+\frac{4691 x}{15625}-\frac{15246}{390625 (5 x+3)}-\frac{1331}{781250 (5 x+3)^2}+\frac{63294 \log (5 x+3)}{390625} \]
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Rubi [A] time = 0.0336888, antiderivative size = 66, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045, Rules used = {88} \[ -\frac{648 x^5}{625}+\frac{513 x^4}{625}+\frac{2826 x^3}{3125}-\frac{7617 x^2}{6250}+\frac{4691 x}{15625}-\frac{15246}{390625 (5 x+3)}-\frac{1331}{781250 (5 x+3)^2}+\frac{63294 \log (5 x+3)}{390625} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(1-2 x)^3 (2+3 x)^4}{(3+5 x)^3} \, dx &=\int \left (\frac{4691}{15625}-\frac{7617 x}{3125}+\frac{8478 x^2}{3125}+\frac{2052 x^3}{625}-\frac{648 x^4}{125}+\frac{1331}{78125 (3+5 x)^3}+\frac{15246}{78125 (3+5 x)^2}+\frac{63294}{78125 (3+5 x)}\right ) \, dx\\ &=\frac{4691 x}{15625}-\frac{7617 x^2}{6250}+\frac{2826 x^3}{3125}+\frac{513 x^4}{625}-\frac{648 x^5}{625}-\frac{1331}{781250 (3+5 x)^2}-\frac{15246}{390625 (3+5 x)}+\frac{63294 \log (3+5 x)}{390625}\\ \end{align*}
Mathematica [A] time = 0.0320577, size = 63, normalized size = 0.95 \[ \frac{-101250000 x^7-41343750 x^6+148050000 x^5+15815625 x^4-81707500 x^3+53587800 x^2+83293560 x+632940 (5 x+3)^2 \log (6 (5 x+3))+21586298}{3906250 (5 x+3)^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 51, normalized size = 0.8 \begin{align*}{\frac{4691\,x}{15625}}-{\frac{7617\,{x}^{2}}{6250}}+{\frac{2826\,{x}^{3}}{3125}}+{\frac{513\,{x}^{4}}{625}}-{\frac{648\,{x}^{5}}{625}}-{\frac{1331}{781250\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{15246}{1171875+1953125\,x}}+{\frac{63294\,\ln \left ( 3+5\,x \right ) }{390625}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.06622, size = 69, normalized size = 1.05 \begin{align*} -\frac{648}{625} \, x^{5} + \frac{513}{625} \, x^{4} + \frac{2826}{3125} \, x^{3} - \frac{7617}{6250} \, x^{2} + \frac{4691}{15625} \, x - \frac{121 \,{\left (1260 \, x + 767\right )}}{781250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac{63294}{390625} \, \log \left (5 \, x + 3\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.31973, size = 243, normalized size = 3.68 \begin{align*} -\frac{20250000 \, x^{7} + 8268750 \, x^{6} - 29610000 \, x^{5} - 3163125 \, x^{4} + 16341500 \, x^{3} + 1532625 \, x^{2} - 126588 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) - 1958490 \, x + 92807}{781250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.12548, size = 56, normalized size = 0.85 \begin{align*} - \frac{648 x^{5}}{625} + \frac{513 x^{4}}{625} + \frac{2826 x^{3}}{3125} - \frac{7617 x^{2}}{6250} + \frac{4691 x}{15625} - \frac{152460 x + 92807}{19531250 x^{2} + 23437500 x + 7031250} + \frac{63294 \log{\left (5 x + 3 \right )}}{390625} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.46116, size = 63, normalized size = 0.95 \begin{align*} -\frac{648}{625} \, x^{5} + \frac{513}{625} \, x^{4} + \frac{2826}{3125} \, x^{3} - \frac{7617}{6250} \, x^{2} + \frac{4691}{15625} \, x - \frac{121 \,{\left (1260 \, x + 767\right )}}{781250 \,{\left (5 \, x + 3\right )}^{2}} + \frac{63294}{390625} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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